Power-Law Martingale

Polynomial growth with an explicit exponent: size is base × iᵖ. It occupies the gap between linear (p = 1) and the geometric curves, and unlike them it never becomes exponential no matter how deep the ladder goes. For operators fitting a curve to backtested behaviour, p is the most surgical control in the catalog.

Size at level i is i raised to p. With p = 2 the curve is quadratic — level 10 is 100× base. p is continuous, so p = 1.3 is a legitimate and much gentler choice than the default, and p below 1 produces a decelerating growth curve.

Below is the wizard's own ladder table and the trading terminal's chart engine, both driven by buildLadderPlan for this mode. Change the level count, spread or target and the rung prices, sizes, capital ramp and chart lines recompute exactly as they would in the grid designer.

Polynomial: total cost grows roughly as nᵖ⁺¹/(p+1). That is far kinder than geometric growth at depth, and it is the reason power mode can support deeper ladders than Fibonacci or geometric at the same budget.

Read the cost vs 5 levels column as the escalation test. A flat ladder doubles when the depth doubles; anything materially above that is a curve whose coverage has to be bought rather than simply configured.

With every rung filled, the volume-weighted average entry is 92.14 against a base of 100 and a deepest rung of 90.00 — so the average sits 79% of the way down the covered range. Getting back to flat from the bottom therefore needs a 2.38% bounce, against 5.00% for a flat ladder of the same depth — 2.62% less work.

Size follows i^p. With p = 2 it is quadratic — between linear and exponential; raising p approaches exponential aggression without ever reaching compounding growth.

The last row is the metric that separates modes. Profit for a full cycle is the target percentage of deployed capital in every mode, so it cannot discriminate. What differs is how much capital has to sit reserved to earn one shallow cycle: this mode reserves 385× base to collect 0.3 bps of it when the first rung completes.

Instruments whose pullback distribution you have actually measured. Power sizing is the natural expression of "I want size to scale with depth to some measured degree" rather than "I want a named curve".

Size follows i^p. With p=2 it sits between linear and exponential; higher p approaches exponential aggression. Useful for custom, backtested risk curves.

Convex but sub-exponential, so the tail is heavy without being unbounded in the compounding sense. The main hazard is p left at the default 2 by operators who wanted "a bit more than linear" — quadratic is considerably more than a bit.

This is the product's grid backtester, not a summary of one. It fetches public candles for the instrument you pick, rebuilds the ladder anchored on the first candle of the window, then applies the engine's own fill, take-profit, refill and stop-loss rules bar by bar. The caveat block inside the panel is part of the output — read it before trusting a number.

First the arithmetic, then the market. The table below is computed from the size curves alone; the sweep underneath replays every one of those ladders over the same real candle window, with grid_mode as the only variable.

• You are deliberately fitting a curve shape to measured pullback behaviour.
• You want super-linear growth that stays polynomial at any depth.
• You need a single continuous parameter to express the whole curve in a review.

• You are not measuring the result — this mode exists for people fitting a curve deliberately.
• You need the multiple partial exits that linear martingale provides; power mode is single-order.

• Default p = 2 is quadratic. If you wanted "slightly more than linear", set p to 1.2–1.4 and measure.
• p below 1 turns this into a decelerating growth curve — a legitimate middle ground between linear and square-root.
• Always re-read the capital table after changing p; the exponent acts on every level at once.

This mode is parametric. The wizard and the settings panel show only the dial(s) it actually uses, and changing one is a structural edit — the resting ladder is cancelled and re-placed at the new sizes.

• Log p with the mode in deployment notes; the curve is meaningless without it.
• Watch the deepest filled level, not the P&L. Depth is the leading indicator; P&L is the lagging one.
• Compare peak committed notional against the account, weekly. A growth curve that has never been deep has never been tested.
• Treat every level increase as a capital decision: adding levels to a growth curve is not a linear cost.

1. 1
   Default-exponent drift

   The mode is chosen for flexibility and then left at p = 2, producing a quadratic ramp nobody explicitly approved.
2. 2
   Depth × exponent interaction

   Raising both depth and p at once multiplies the effect. Change one at a time and re-measure.

• Spread sets how fast the ladder consumes depth. Widening it buys coverage for the same level count at the cost of fewer fills.
• Target sets what each cycle books. Below round-trip fees plus slippage, a grid is a fee generator regardless of the size curve.
• The stop loss is the only bound on the tail. Without it, the curve's worst case is whatever the market does, not what you planned.

1. 1
   How do I choose p?

   Run the sweep below at several depths, then pick the smallest p whose measured recovery advantage over linear still justifies its capital requirement. The answer is usually lower than people expect.

• Sizes and capital: levelMultiplier / gridModeCurve in lib/grid/gridModes.ts, mirrored from grid_modes.hpp and the Python engine's lot calculator.
• Rung and exit prices, capital ramp, init targets and the stop line: buildLadderPlan — the same builder the wizard and grid designer use.
• Backtest fills, cycles and P&L: runBacktest / runBacktestSweep over public broker candles, applying the engine's fill, exit, refill and stop rules.
• Price charts: the trading terminal's chart engine, with the ladder drawn through its own price-line API.

• 1.Grid Modes — Overview — The full taxonomy and how to choose
• 2.Martingale family — What every curve in this family has in common
• 3.Capital Allocation — Sizing an account to a Power-Law Martingale ladder
• 4.Stop Loss — Bounding this curve's tail
• 5.Reading the Ladder Plan — Verifying the curve before deploying
• 6.Grid Structure — Levels, init batch and base size